Consider an elliptic curve defined over an imaginary quadratic field with good reduction at the primes above and with complex multiplication by the full ring of integers of . In this paper, we construct -adic analogues of the Eisenstein–Kronecker series for such an elliptic curve as Coleman functions on the elliptic curve. We then prove -adic analogues of the first and second Kronecker limit formulas by using the distribution relation of the Kronecker theta function.
"-adic Eisenstein–Kronecker series for CM elliptic curves and the Kronecker limit formulas." Nagoya Math. J. 219 269 - 302, September 2015. https://doi.org/10.1215/00277630-2891995